3. int sin^3 х * cos^2 x dx = int sin^2 x * cos^2 x * sin x dx =
= int sin^2 x * cos^2 x d(-cos x) = -int sin^2 x * cos^2 x d(cos x) =
= -int (1 - cos^2 x) * cos^2 x d(cos x) = | t = cos x | =
= -int (1 - t^2) * t^2 dt = -int (t^2 - t^4) dt = -(1/3 * t^3 - 1/5 * t^5) + C =
= 1/5 * t^5 - 1/3 * t^3 + C = | t = cos x | = 1/5 * cos^5 x - 1/3 * cos^3 x + C